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Sep 20, 2013
09/13

by
Ruth Durrer

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I discuss the generation of a stochastic background of gravitational waves during a first order phase transition. I present simple general arguments which explain the main features of the gravitational wave spectrum like the $k^3$ power law growth on large scales and a estimate for the peak amplitude. In the second part I concentrate on the electroweak phase transition and argue that the nucleosynthesis bound on its gravitational wave background seriously limits seed magnetic fields which may...

Source: http://arxiv.org/abs/1002.1389v1

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Sep 19, 2013
09/13

by
Ruth Durrer

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This course is an introduction to the physics of braneworlds. We concentrate on braneworlds with only one extra-dimension and discuss their gravity. We derive the gravitational equations on the brane from the bulk Einstein equation and explore some limits in which they reduce to 4-dimensional Einstein gravity. We indicate how cosmological perturbations from braneworlds are probably very different from usual cosmological perturbations and give some examples of the preliminary results in this...

Source: http://arxiv.org/abs/hep-th/0507006v1

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Jul 20, 2013
07/13

by
Ruth Durrer

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We discuss gravitational effects of global scalar fields and, especially, of global topological defects. We first give an introduction to the dynamics of global fields and the formation of defects. Next we investigate the induced gravitational fields, first in a flat background and then in the expanding universe. In flat space, we explicitly calculate the gravitational fields of exact global monopole and global texture solutions and discuss the motion of photons and massive particles in these...

Source: http://arxiv.org/abs/astro-ph/9411010v1

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Jun 27, 2018
06/18

by
Ruth Durrer

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This review describes the discovery of the cosmic microwave background radiation in 1965 and its impact on cosmology in the 50 years that followed. This discovery has established the Big Bang model of the Universe and the analysis of its fluctuations has confirmed the idea of inflation and led to the present era of precision cosmology. I discuss the evolution of cosmological perturbations and their imprint on the CMB as temperature fluctuations and polarization. I also show how a phase of...

Topics: High Energy Physics - Phenomenology, Cosmology and Nongalactic Astrophysics, Astrophysics, General...

Source: http://arxiv.org/abs/1506.01907

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Sep 19, 2013
09/13

by
Ruth Durrer

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An introduction to topological defects in cosmology is given. We discuss their possible relevance for structure formation. Especial emphasis is given on the signature of topological defects in the spectrum of anisotropies in the cosmic microwave background. We present simple analytic estimates for the CMB spectrum on large and intermediate scales and compare them with the corresponding approximations for models where initial perturbations are generated during an inflationary epoch.

Source: http://arxiv.org/abs/astro-ph/9703001v1

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Sep 22, 2013
09/13

by
Ruth Durrer

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In this talk I summarize the topics addressed during the conference. We have discussed the most relevant cosmological observations of the last say 10 years and their implications for our understanding of the Universe. My finding throughout this meeting has been that it is amazing how our knowledge of cosmological parameters has improved during the last years. It comes as a surprise to many, that the simplest inflationary model of adiabatic perturbations agrees well with present data. But it is...

Source: http://arxiv.org/abs/astro-ph/0205101v1

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Sep 21, 2013
09/13

by
Ruth Durrer

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This is a review on cosmological perturbation theory. After an introduction, it presents the problem of gauge transformation. Gauge invariant variables are introduced and the Einstein and conservation equations are written in terms of these variables. Some examples, especially perfect fluids and scalar fields are presented in detail. The generation of perturbations during inflation is studied. Lightlike geodesics and their relevance for CMB anisotropies are briefly discussed. Perturbation...

Source: http://arxiv.org/abs/astro-ph/0402129v2

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Sep 21, 2013
09/13

by
Ruth Durrer

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The cosmic microwave background (CMB) anisotropies have turned out to represent one of the most stringent 'bottle necks' for scenarios of large scale structure formation. As a possibility to relax this constraint, it has been proposed that early reionization can damp CMB fluctuations on small scales due to photon diffusion in the ionized plasma. As an example, I investigate the recently proposed scenario with cold dark matter (CDM) and texture seeds. There, an analysis of CMB anisotropies shows...

Source: http://arxiv.org/abs/astro-ph/9311039v1

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Sep 21, 2013
09/13

by
Ruth Durrer

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After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the...

Source: http://arxiv.org/abs/astro-ph/9311041v1

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Sep 22, 2013
09/13

by
Ruth Durrer

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In this paper I discuss what we truly know about dark energy. I shall argue that up to date our single indication for the existence of dark energy comes from distance measurements and their relation to redshift. Supernovae, CMB anisotropies and observations of baryon acoustic oscillations, they all simply tell us that the observed distance to a given redshift is larger than the one expected from a Friedmann Lemaitre universe with matter only and the locally measured Hubble parameter.

Source: http://arxiv.org/abs/1103.5331v3

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Sep 20, 2013
09/13

by
Ruth Durrer

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The analysis of anisotropies in the cosmic microwave background (CMB) has become an extremely valuable tool for cosmology. We even have hopes that planned CMB anisotropy experiments may revolutionize cosmology. Together with determinations of the CMB spectrum, they represent the first cosmological precision measurements. This is illustrated in the talk by Anthony Lasenby. The value of CMB anisotropies lies to a big part in the simplicity of the theoretical analysis. Fluctuations in the CMB can...

Source: http://arxiv.org/abs/astro-ph/9610234v1

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Jul 19, 2013
07/13

by
Ruth Durrer

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In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables. The resulting scalar, vector and tensor equations are supplemented by simple examples for illustration. The gravity wave example may be of more than academic interest and even represent a new way to detect gravitational waves.

Source: http://arxiv.org/abs/astro-ph/9401033v1

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Sep 23, 2013
09/13

by
Ruth Durrer

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The physics of the origin and evolution of CMB anisotropies is described. I explain the idea and status of cosmic parameter estimation and follow it up with critical comments on its dependence on model assumptions and initial conditions.

Source: http://arxiv.org/abs/astro-ph/0109274v1

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Sep 23, 2013
09/13

by
Ruth Durrer

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This is a review of the theory of CMB anisotropies, an updated version of a course given at the troisieme cycle de la Suisse Romande. An introduction to gauge invariant cosmological perturbation theory is given and the theory CMB anisotropies is develiped in this context. Simple analytical approximations for the acoustic peak positions for adiabatic and isocurvature perturbations are derived. Silk damping is discussed by an analytic approximation. A short description of the present status of...

Source: http://arxiv.org/abs/astro-ph/0109522v1

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Sep 22, 2013
09/13

by
Ruth Durrer

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Structure formation with topological defects is described. The main differences from inflationary models are highlighted. The results are compared with recent observations. It is concluded that all the defect models studied so far are in disagreement with recent observations of CMB anisotropies. Furthermore, present observations do not support 'decoherence', a generic feature of structure formation from topological defects.

Source: http://arxiv.org/abs/astro-ph/0003363v1

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Jul 20, 2013
07/13

by
Ruth Durrer

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I describe the imprint of primordial magnetic fields on the CMB. I show that these are observable only if the field amplitude is of the order of $B\gsim 10^{-9}G$ on Mpc scale. I further argue that such fields are strongly constrained by the stochastic background of gravity waves which they produce. Primordial magnetic fields, which are strong enough to be seen in the CMB, are compatible with the nucleosynthesis bound, only if their spectrum is close to scale invariant, or maybe if helical...

Source: http://arxiv.org/abs/astro-ph/0609216v1

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Jun 30, 2018
06/18

by
Elena Sellentin; Ruth Durrer

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Three relativistic particles in addition to the photon are detected in the cosmic microwave background (CMB). In the standard model of cosmology, these are interpreted as the three neutrino species. However, at the time of CMB-decoupling, neutrinos are not only relativistic but they are also freestreaming. Here, we investigate, whether the CMB is sensitive to this defining feature of neutrinos, or whether the CMB-data allow to replace neutrinos with a relativistic fluid. We show that free...

Topics: High Energy Physics - Phenomenology, Astrophysics, General Relativity and Quantum Cosmology,...

Source: http://arxiv.org/abs/1412.6427

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Sep 22, 2013
09/13

by
Martin Kunz; Ruth Durrer

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We present an analysis of CMB anisotropies induced by global scalar fields in the large N limit. In this limit, the CMB anisotropy spectrum can be determined without cumbersome 3D simulations. We determine the source functions and their unequal time correlation functions and show that they are quite similar to the corresponding functions in the texture model. This leads us to the conclusion that the large N limit provides a 'cheap approximation' to the texture model of structure formation.

Source: http://arxiv.org/abs/astro-ph/9612202v1

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Sep 21, 2013
09/13

by
Ruth Durrer; Massimiliano Rinaldi

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We discuss the creation of massless particles in a Universe, which transits from a radiation-dominated era to any other expansion law. We calculate in detail the generation of gravitons during the transition to a matter dominated era. We show that the resulting gravitons generated in the standard radiation/matter transition are negligible. We use our result to constrain one or more previous matter dominated era, or any other expansion law, which may have taken place in the early Universe. We...

Source: http://arxiv.org/abs/0901.0650v2

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Sep 18, 2013
09/13

by
Ruth Durrer; Joachim Laukenmann

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The aim of this paper is to show, that the 'oscillating universe' is a viable alternative to inflation. We remind that this model provides a natural solution to the flatness or entropy and to the horizon problem of standard cosmology. We study the evolution of density perturbations and determine the power spectrum in a closed universe. The results lead to constraints of how a previous cycle might have looked like. We argue that most of the radiation entropy of the present universe may have...

Source: http://arxiv.org/abs/gr-qc/9510041v2

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Sep 22, 2013
09/13

by
Chiara Caprini; Ruth Durrer

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We compute the gravity waves induced by anisotropic stresses of stochastic primordial magnetic fields. The nucleosynthesis bound on gravity waves is then used to derive a limit on the magnetic field amplitude as function of the spectral index. The obtained limits are extraordinarily strong: If the primordial magnetic field is produced by a causal process, leading to a spectral index $n\ge 2$ on super horizon scales, galactic magnetic fields produced at the electroweak phase transition or...

Source: http://arxiv.org/abs/astro-ph/0106244v2

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Sep 20, 2013
09/13

by
Raphael Lamon; Ruth Durrer

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We consider super-gravity models in which the lightest supersymmetric particle (LSP) is a stable gravitino. The next-to-lightest supersymmetric particle (NLSP) freezes out with its thermal relic density and then decays after $(10^5-10^{10})$ sec, injecting high-energy photons into the cosmic plasma. These photons heat up the electron plasma which then thermalizes with the cosmic microwave background (CMB) via Compton scattering, bremsstrahlung and double-Compton scattering. Contrary to previous...

Source: http://arxiv.org/abs/hep-ph/0506229v4

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Jun 27, 2018
06/18

by
Francesco Montanari; Ruth Durrer

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We investigate how the lensing potential can be measured tomographically with future galaxy surveys using their number counts. Such a measurement is an independent test of the standard $\Lambda$CDM framework and can be used to discern modified theories of gravity. We perform a Fisher matrix forecast based on galaxy angular-redshift power spectra, assuming specifications consistent with future photometric Euclid-like surveys and spectroscopic SKA-like surveys. For the Euclid-like survey we...

Topics: Cosmology and Nongalactic Astrophysics, Astrophysics

Source: http://arxiv.org/abs/1506.01369

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Sep 18, 2013
09/13

by
Marcus Ruser; Ruth Durrer

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We consider a two-brane system in a five-dimensional anti-de Sitter spacetime. We study particle creation due to the motion of the physical brane which first approaches the second static brane (contraction) and then recedes from it(expansion). The spectrum and the energy density of the generated gravitons are calculated. We show that the massless gravitons have a blue spectrum and that their energy density satisfies the nucleosynthesis bound with very mild constraints on the parameters. We also...

Source: http://arxiv.org/abs/0704.0790v3

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Jul 20, 2013
07/13

by
Ruth Durrer; Mairi Sakellariadou

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We study microwave background anisotropies induced by scaling seed perturbations in a universe dominated by cold dark matter. Using a gauge invariant linear perturbation analysis, we solve the perturbation equations on super-horizon scales, for CMB anisotropies triggered by generic gravitational seeds. We find that perturbations induced by seeds --- under very mild restrictions --- are nearly isocurvature. Thus, compensation, which is mainly the consequence of physically sensible initial...

Source: http://arxiv.org/abs/astro-ph/9702028v4

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Sep 22, 2013
09/13

by
Chiara Caprini; Ruth Durrer

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The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does in general not vanish on scales larger than the correlation scale. If the variable is a divergence free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave...

Source: http://arxiv.org/abs/astro-ph/0603476v3

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Sep 18, 2013
09/13

by
Chiara Caprini; Ruth Durrer

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In their recent paper ``Faraday rotation of the cosmic microwave background polarization by a stochastic magnetic field'', Kosowsky et al. Phys.Rev. D71, 043006 (2005) have commented about our paper [C.Caprini and R.Durrer, Phys. Rev. D65, 023517 (2002)], in which we derived very strong limits on the amplitude of a primordial magnetic field from gravitational wave production. They argue that our limits are erroneous. In this short comment we defend our result.

Source: http://arxiv.org/abs/astro-ph/0504553v1

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Sep 17, 2013
09/13

by
Ruth Durrer; Chiara Caprini

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We discuss the implications of causality on a primordial magnetic field. We show that the residual field on large scales is much more suppressed than usually assumed and that a helical component is even more reduced. Due to this strong suppression, even maximal primordial fields generated at the electroweak phase transition can just marginally seed the fields in clusters, but they cannot leave any detectable imprint on the cosmic microwave background.

Source: http://arxiv.org/abs/astro-ph/0305059v2

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Sep 22, 2013
09/13

by
Ruth Durrer; Mairi Sakellariadou

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We compute the energy spectra for massless Kalb-Ramond axions in four-dimensional anisotropic string cosmological models. We show that, when integrated over directions, the four-dimensional anisotropic model leads to infra-red divergent spectra similar to the one found in the isotropic case.

Source: http://arxiv.org/abs/hep-ph/0003112v1

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Sep 17, 2013
09/13

by
Ruth Durrer; Roy Maartens

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Observations provide increasingly strong evidence that the universe is accelerating. This revolutionary advance in cosmological observations confronts theoretical cosmology with a tremendous challenge, which it has so far failed to meet. Explanations of cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are nearly all based on a dark energy field with fine-tuned, unnatural properties. There is a great variety of models, but...

Source: http://arxiv.org/abs/0711.0077v2

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Jun 29, 2018
06/18

by
Ruth Durrer; Vittorio Tansella

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We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We...

Topics: Astrophysics, Cosmology and Nongalactic Astrophysics

Source: http://arxiv.org/abs/1605.05974

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Sep 18, 2013
09/13

by
Lukas Lichtensteiger; Ruth Durrer

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We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can then be compactified and can be identified topologically (but not metrically!) with a three sphere. Therefore, at fixed time, the winding of the map is defined. We investigate whether static solutions with non-trivial winding number exist. The answer which we...

Source: http://arxiv.org/abs/astro-ph/9901024v1

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Sep 18, 2013
09/13

by
Ruth Durrer; Marcus Ruser

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In braneworld cosmology the expanding Universe is realized as a brane moving through a warped higher-dimensional spacetime. Like a moving mirror causes the creation of photons out of vacuum fluctuations, a moving brane leads to graviton production. We show that, very generically, Kaluza-Klein (KK) particles scale like stiff matter with the expansion of the Universe and can therefore not represent the dark matter in a warped braneworld. We present results for the production of massless and KK...

Source: http://arxiv.org/abs/0704.0756v3

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Sep 18, 2013
09/13

by
Elisa Fenu; Ruth Durrer

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The energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress and therefore generates gravitational waves. It has been argued in the literature (Caprini & Durrer \cite{CD}) that this gravitational wave production can be very strong and that back-reaction cannot be neglected. On the other hand, a gravitational wave background does affect the evolution of magnetic fields. It has also been argued (Tsagas et al....

Source: http://arxiv.org/abs/0809.1383v3

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Sep 17, 2013
09/13

by
Ruth Durrer; Philippe Kocian

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In this letter we calculate the emission of gravity waves by the binary pulsar in the framework of five dimensional braneworlds. We consider only spacetimes with one compact extra-dimension. We show that the presence of additional degrees of freedom, especially the 'gravi-scalar' leads to a modification of Einstein's quadrupole formula. We compute the induced change for the binary pulsar PSR 1913+16 where it amounts to about 20% which is by far excluded by present experimental data.

Source: http://arxiv.org/abs/hep-th/0305181v2

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Sep 23, 2013
09/13

by
Camille Bonvin; Ruth Durrer

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In this paper we compute the quantity which is truly measured in a large galaxy survey. We take into account the effects coming from the fact that we actually observe galaxy redshifts and sky positions and not true spatial positions. Our calculations are done within linear perturbation theory for both the metric and the observer velocities but they can be used for non-linear matter power spectra. We shall see that the complications due to the fact that we only observe on our background...

Source: http://arxiv.org/abs/1105.5280v3

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Sep 22, 2013
09/13

by
Cyril Cartier; Ruth Durrer

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We show that scalar as well as vector and tensor metric perturbations in the Randall-Sundrum II braneworld allow normalizable tachyonic modes, i.e., possible instabilities. These instabilities require nonvanishing initial anisotropic stresses on the brane. We show with a specific example that within the Randall-Sundrum II model, even though the tachyonic modes are excited, no instability develops. We argue, however, that in the cosmological context instabilities might in principle be present....

Source: http://arxiv.org/abs/hep-th/0409287v2

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Sep 23, 2013
09/13

by
Ruth Durrer; Jasper Hasenkamp

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We provide a simple transfer function that determines the effect of an early matter dominated era on the gravitational wave background and show that a large class of compactifications of superstring theory might be tested by observations of the gravitational wave background from inflation. For large enough reheating temperatures $> 10^9 \GeV$ the test applies to all models containing at least one scalar with mass $ < 10^{12}\GeV$ that acquires a large initial oscillation amplitude after...

Source: http://arxiv.org/abs/1105.5283v3

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Sep 23, 2013
09/13

by
Francesco Montanari; Ruth Durrer

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The fitting formula for the location of the first acoustic peak in the matter power spectrum is revised. We discuss the physics that leads to baryon acoustic oscillations: the recombination history, the tight coupling approximation and the velocity overshoot effect. A new fitting formula is proposed, which is in accordance within 5% with numerical results for a suitable range of cosmological parameters, whereas previous results yield deviations of up to 20%. The crucial improvement turns out to...

Source: http://arxiv.org/abs/1105.1514v3

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Sep 22, 2013
09/13

by
Ruth Durrer; Roy Maartens

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Explanations of the late-time cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are mostly based on a dark energy field with fine-tuned, unnatural properties. There is a great variety of models, but all share one feature in common -- an inability to account for the gravitational properties of the vacuum energy, and a failure to solve the so-called coincidence problem. Two broad alternatives to dark energy have emerged as...

Source: http://arxiv.org/abs/0811.4132v1

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Jul 22, 2013
07/13

by
Ruth Durrer; Tina Kahniashvili

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Anisotropies in the cosmic microwave background radiation due to gravity waves are investigated. An initial spectrum of gravity waves may have been induced during an epoch of inflation. We study the propagation of such a spectrum in a Friedmann background of hot and cold dark matter, radiation and (possibly) a cosmological constant. We finally calculate its imprint as anisotropies on the cosmic microwave background. We also take into account that massless particles can source gravity waves by...

Source: http://arxiv.org/abs/astro-ph/9702226v2

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Sep 21, 2013
09/13

by
Ruth Durrer; Martin Kunz

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In this work we present a partially new method to analyze fluctuations which are induced by causal scaling seeds. We show that the power spectra due to this kind of seed perturbations are determined by five analytic functions, which we determine numerically for a special example. We put forward the view that, even if recent work disfavors the models with cosmic strings and global O(4) texture, causal scaling seed perturbations merit a more thorough and general analysis, which we initiate in...

Source: http://arxiv.org/abs/astro-ph/9711133v1

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Sep 23, 2013
09/13

by
Jose Beltrán Jiménez; Ruth Durrer

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n this paper we study the effect of biasing on the power spectrum at large scales. We show that even though non-linear biasing does introduce a white noise contribution on large scales, the $P(k)\propto k^n$ behavior of the matter power spectrum on large scales may still be visible and above the white noise for about one decade. We show, that the Kaiser biasing scheme which leads to linear bias of the correlation function on {\em large} scales, also generates a linear bias of the {\rm power...

Source: http://arxiv.org/abs/1006.2343v3

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Jun 29, 2018
06/18

by
Azadeh Moradinezhad Dizgah; Ruth Durrer

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We study the impact of the often neglected lensing contribution to galaxy number counts on the $E_g$ statistics which is used to constrain deviations from GR. This contribution affects both the galaxy-galaxy and the convergence-galaxy spectra, while it is larger for the latter. At higher redshifts probed by upcoming surveys, neglecting this term induces a substantial error in the spectra and therefore on the $E_g$ statistics which is constructed from the combination of the two. Moreover,...

Topics: Astrophysics, Cosmology and Nongalactic Astrophysics

Source: http://arxiv.org/abs/1604.08914

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Jun 29, 2018
06/18

by
Jeppe Trøst Nielsen; Ruth Durrer

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We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our derivation to higher order terms, especially the third order number counts which are needed to compute the 1-loop contribution to the power spectrum.

Topics: Astrophysics, Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1606.02113

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Sep 19, 2013
09/13

by
Ruth Durrer; Francesco Sylos Labini

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In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D=2. Our idea can also be interpreted as a redefinition of the notion of bias.

Source: http://arxiv.org/abs/astro-ph/9804171v2

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Sep 19, 2013
09/13

by
Kerstin E. Kunze; Ruth Durrer

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In this letter we investigate whether the isotropy problem is naturally solved in inflationary cosmologies inspired by string theory, so called pre-big-bang cosmologies. We find that, in contrast to what happens in the more common 'potential inflation' models, initial anisotropies do not decay during pre-big-bang inflation.

Source: http://arxiv.org/abs/gr-qc/9912081v1

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Sep 20, 2013
09/13

by
Enea Di Dio; Ruth Durrer

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We compute the vector and tensor contributions to the luminosity distance fluctuations in first order perturbation theory and we expand them in spherical harmonics. This work presents the formalism with a first application to a stochastic background of primordial gravitational waves.

Source: http://arxiv.org/abs/1205.3366v3

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Jul 20, 2013
07/13

by
Ruth Durrer; Zhi-hong Zhou

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The topic of this letter is structure formation with topological defects. We first present a partially new, fully local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced by topological defects (or any other type of seeds). We show that this treatment is extremly well suited for linear numerical analysis of structure formation by applying it to the texture scenario. Our numerical results cover a larger dynamical range than...

Source: http://arxiv.org/abs/astro-ph/9407027v1

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Sep 24, 2013
09/13

by
Camille Bonvin; Chiara Caprini; Ruth Durrer

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We compute the contribution to the scalar metric perturbations from large-scale magnetic fields which are generated during inflation. We show that apart from the usual passive and compensated modes, the magnetic fields also contribute to the constant mode from inflation. This is different from the causal (post inflationary) generation of magnetic fields where such a mode is absent and it might lead to significant, non-Gaussian CMB anisotropies.

Source: http://arxiv.org/abs/1112.3901v3